Convexity and Gamma

Convexity and Gamma describe the non-linear relationship between an option's price and the price of the underlying asset. Gamma specifically measures the rate of change in an option's delta as the underlying price moves.

A position with high positive gamma means the delta changes rapidly, which can be profitable for the holder as the position becomes more sensitive to favorable moves. Conversely, short gamma positions are dangerous because they require constant hedging, which becomes increasingly expensive as the underlying moves against the position.

In options trading, understanding gamma is crucial for managing the risk of sudden, large price moves. It is the key to understanding why options are non-linear instruments and how they can be used to manage risk or enhance returns.